scholarly journals Comparison of ensemble Kalman filter and variational approaches for CO<sub>2</sub> data assimilation

2013 ◽  
Vol 13 (5) ◽  
pp. 12825-12865
Author(s):  
A. Chatterjee ◽  
A. M. Michalak
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Weather Prediction ◽  
Co2 Flux ◽  
Estimation Problem ◽  
Advantages And Disadvantages ◽  
Flux Estimation ◽  
Operational Constraints ◽  
The Impact

Abstract. Data assimilation (DA) approaches, such as the variational and the ensemble Kalman filter, provide a computationally efficient framework for solving the CO2 source-sink estimation problem. Unlike DA applications for weather prediction and constituent assimilation, however, the advantages and disadvantages of alternative DA approaches for CO2 flux estimation have not been extensively explored. In this study, we compare and assess estimates from two advanced DA methods (an ensemble square root filter and a variational technique) using a simple 1-dimensional advection-diffusion inverse problem that has been designed to capture the nuances of a real CO2 flux estimation problem. Experiments are specifically designed to identify the impact of the observational density, heterogeneity, and uncertainty, as well as operational constraints (i.e., ensemble size, number of descent iterations) in order to isolate the degradation in the DA estimates relative to the estimates from a batch inverse modeling scheme. No dynamical model is explicitly specified for the DA methods to keep the problem setup analogous to a real CO2 flux estimation problem. Results demonstrate that the performance of the DA approaches depends on a complex interplay between the measurement network and the operational constraints imposed to make the DA algorithms practically feasible. The overall advantages/disadvantages of the two examined DA approaches are complementary and highlight that, specifically for CO2 applications, selection of one method over the other should be dictated by the carbon science questions being asked, and the inversion conditions under which the approaches are being applied.

scholarly journals Technical Note: Comparison of ensemble Kalman filter and variational approaches for CO<sub>2</sub> data assimilation

2013 ◽  
Vol 13 (23) ◽  
pp. 11643-11660 ◽  
Author(s):  
A. Chatterjee ◽  
A. M. Michalak
Keyword(s):  
Kalman Filter ◽  
Inverse Modeling ◽  
Ensemble Kalman Filter ◽  
Co2 Flux ◽  
Estimation Problem ◽  
Square Root ◽  
Flux Estimation ◽  
Source Sink ◽  
Operational Constraints ◽  
Square Root Filter

Abstract. Data assimilation (DA) approaches, including variational and the ensemble Kalman filter methods, provide a computationally efficient framework for solving the CO2 source–sink estimation problem. Unlike DA applications for weather prediction and constituent assimilation, however, the advantages and disadvantages of DA approaches for CO2 flux estimation have not been extensively explored. In this study, we compare and assess estimates from two advanced DA approaches (an ensemble square root filter and a variational technique) using a batch inverse modeling setup as a benchmark, within the context of a simple one-dimensional advection–diffusion prototypical inverse problem that has been designed to capture the nuances of a real CO2 flux estimation problem. Experiments are designed to identify the impact of the observational density, heterogeneity, and uncertainty, as well as operational constraints (i.e., ensemble size, number of descent iterations) on the DA estimates relative to the estimates from a batch inverse modeling scheme. No dynamical model is explicitly specified for the DA approaches to keep the problem setup analogous to a typical real CO2 flux estimation problem. Results demonstrate that the performance of the DA approaches depends on a complex interplay between the measurement network and the operational constraints. Overall, the variational approach (contingent on the availability of an adjoint transport model) more reliably captures the large-scale source–sink patterns. Conversely, the ensemble square root filter provides more realistic uncertainty estimates. Selection of one approach over the other must therefore be guided by the carbon science questions being asked and the operational constraints under which the approaches are being applied.

scholarly journals Scale-Dependent Representation of the Information Content of Observations in the Global Ensemble Kalman Filter Data Assimilation

2016 ◽  
Vol 144 (8) ◽  
pp. 2927-2945
Author(s):  
Nedjeljka Žagar ◽  
Jeffrey Anderson ◽  
Nancy Collins ◽  
Timothy Hoar ◽  
Kevin Raeder ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Information Content ◽  
Ensemble Kalman Filter ◽  
Large Scale ◽  
Variance Reduction ◽  
Weather Prediction ◽  
Current Data ◽  
Model Framework ◽  
The Tropics

Abstract Global data assimilation systems for numerical weather prediction (NWP) are characterized by significant uncertainties in tropical analysis fields. Furthermore, the largest spread of global ensemble forecasts in the short range on all scales is in the tropics. The presented results suggest that these properties hold even in the perfect-model framework and the ensemble Kalman filter data assimilation with a globally homogeneous network of wind and temperature profiles. The reasons for this are discussed by using the modal analysis, which provides information about the scale dependency of analysis and forecast uncertainties and information about the efficiency of data assimilation to reduce the prior uncertainties in the balanced and inertio-gravity dynamics. The scale-dependent representation of variance reduction of the prior ensemble by the data assimilation shows that the peak efficiency of data assimilation is on the synoptic scales in the midlatitudes that are associated with quasigeostrophic dynamics. In contrast, the variance associated with the inertia–gravity modes is less successfully reduced on all scales. A smaller information content of observations on planetary scales with respect to the synoptic scales is discussed in relation to the large-scale tropical uncertainties that current data assimilation methodologies do not address successfully. In addition, it is shown that a smaller reduction of the large-scale uncertainties in the prior state for NWP in the tropics than in the midlatitudes is influenced by the applied radius for the covariance localization.

scholarly journals An Ensemble Kalman Filter for severe dust storm data assimilation over China

2008 ◽  
Vol 8 (11) ◽  
pp. 2975-2983 ◽  
Author(s):  
C. Lin ◽  
Z. Wang ◽  
J. Zhu
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Dust Storm ◽  
Ensemble Kalman Filter ◽  
Deposition Velocity ◽  
Dust Storms ◽  
Initial Time ◽  
Model Errors ◽  
The Impact ◽  
Severe Dust Storm

Abstract. An Ensemble Kalman Filter (EnKF) data assimilation system was developed for a regional dust transport model. This paper applied the EnKF method to investigate modeling of severe dust storm episodes occurring in March 2002 over China based on surface observations of dust concentrations to explore the impact of the EnKF data assimilation systems on forecast improvement. A series of sensitivity experiments using our system demonstrates the ability of the advanced EnKF assimilation method using surface observed PM10 in North China to correct initial conditions, which leads to improved forecasts of dust storms. However, large errors in the forecast may arise from model errors (uncertainties in meteorological fields, dust emissions, dry deposition velocity, etc.). This result illustrates that the EnKF requires identification and correction model errors during the assimilation procedure in order to significantly improve forecasts. Results also show that the EnKF should use a large inflation parameter to obtain better model performance and forecast potential. Furthermore, the ensemble perturbations generated at the initial time should include enough ensemble spreads to represent the background error after several assimilation cycles.

scholarly journals Impact of surface data assimilation using an ensemble Kalman filter technique on the improvement of weather prediction

2019 ◽  
Vol 1127 ◽  
pp. 012041
Author(s):  
N J Trilaksono ◽  
M Taqiyya ◽  
N Dewani ◽  
I D G A Junnaedhi ◽  
E Riawan ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Weather Prediction ◽  
Filter Technique ◽  
Surface Data

E4DVar: Coupling an Ensemble Kalman Filter with Four-Dimensional Variational Data Assimilation in a Limited-Area Weather Prediction Model

2012 ◽  
Vol 140 (2) ◽  
pp. 587-600 ◽  
Author(s):  
Meng Zhang ◽  
Fuqing Zhang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Prediction Model ◽  
Ensemble Kalman Filter ◽  
Weather Prediction ◽  
Coupled System ◽  
Limited Area ◽  
Ensemble Forecasts ◽  
Background Error ◽  
Hybrid Data Assimilation

A hybrid data assimilation approach that couples the ensemble Kalman filter (EnKF) and four-dimensional variational (4DVar) methods is implemented for the first time in a limited-area weather prediction model. In this coupled system, denoted E4DVar, the EnKF and 4DVar systems run in parallel while feeding into each other. The multivariate, flow-dependent background error covariance estimated from the EnKF ensemble is used in the 4DVar minimization and the ensemble mean in the EnKF analysis is replaced by the 4DVar analysis, while updating the analysis perturbations for the next cycle of ensemble forecasts with the EnKF. Therefore, the E4DVar can obtain flow-dependent information from both the explicit covariance matrix derived from ensemble forecasts, as well as implicitly from the 4DVar trajectory. The performance of an E4DVar system is compared with the uncoupled 4DVar and EnKF for a limited-area model by assimilating various conventional observations over the contiguous United States for June 2003. After verifying the forecasts from each analysis against standard sounding observations, it is found that the E4DVar substantially outperforms both the EnKF and 4DVar during this active summer month, which featured several episodes of severe convective weather. On average, the forecasts produced from E4DVar analyses have considerably smaller errors than both of the stand-alone EnKF and 4DVar systems for forecast lead times up to 60 h.

scholarly journals Convective-Scale Data Assimilation for the Weather Research and Forecasting Model Using the Local Particle Filter

2017 ◽  
Vol 145 (5) ◽  
pp. 1897-1918 ◽  
Author(s):  
Jonathan Poterjoy ◽  
Ryan A. Sobash ◽  
Jeffrey L. Anderson
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Weather Prediction ◽  
Squall Line ◽  
Monte Carlo Data ◽  
Mixing Ratios ◽  
Convective Scale ◽  
Non Gaussian ◽  
Mean Square Errors

Abstract Particle filters (PFs) are Monte Carlo data assimilation techniques that operate with no parametric assumptions for prior and posterior errors. A data assimilation method introduced recently, called the local PF, approximates the PF solution within neighborhoods of observations, thus allowing for its use in high-dimensional systems. The current study explores the potential of the local PF for atmospheric data assimilation through cloud-permitting numerical experiments performed for an idealized squall line. Using only 100 ensemble members, experiments using the local PF to assimilate simulated radar measurements demonstrate that the method provides accurate analyses at a cost comparable to ensemble filters currently used in weather models. Comparisons between the local PF and an ensemble Kalman filter demonstrate benefits of the local PF for producing probabilistic analyses of non-Gaussian variables, such as hydrometeor mixing ratios. The local PF also provides more accurate forecasts than the ensemble Kalman filter, despite yielding higher posterior root-mean-square errors. A major advantage of the local PF comes from its ability to produce more physically consistent posterior members than the ensemble Kalman filter, which leads to fewer spurious model adjustments during forecasts. This manuscript presents the first successful application of the local PF in a weather prediction model and discusses implications for real applications where nonlinear measurement operators and nonlinear model processes limit the effectiveness of current Gaussian data assimilation techniques.

A Non-Gaussian Ensemble Filter Update for Data Assimilation

2010 ◽  
Vol 138 (11) ◽  
pp. 4186-4198 ◽  
Author(s):  
Jeffrey L. Anderson
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Sampling Error ◽  
Weather Prediction ◽  
Large Ensembles ◽  
Stochastic Filter ◽  
Pathological Behavior ◽  
Non Gaussian ◽  
Observation Space

Abstract A deterministic square root ensemble Kalman filter and a stochastic perturbed observation ensemble Kalman filter are used for data assimilation in both linear and nonlinear single variable dynamical systems. For the linear system, the deterministic filter is simply a method for computing the Kalman filter and is optimal while the stochastic filter has suboptimal performance due to sampling error. For the nonlinear system, the deterministic filter has increasing error as ensemble size increases because all ensemble members but one become tightly clustered. In this case, the stochastic filter performs better for sufficiently large ensembles. A new method for computing ensemble increments in observation space is proposed that does not suffer from the pathological behavior of the deterministic filter while avoiding much of the sampling error of the stochastic filter. This filter uses the order statistics of the prior observation space ensemble to create an approximate continuous prior probability distribution in a fashion analogous to the use of rank histograms for ensemble forecast evaluation. This rank histogram filter can represent non-Gaussian observation space priors and posteriors and is shown to be competitive with existing filters for problems as large as global numerical weather prediction. The ability to represent non-Gaussian distributions is useful for a variety of applications such as convective-scale assimilation and assimilation of bounded quantities such as relative humidity.

scholarly journals E3DVar: Coupling an Ensemble Kalman Filter with Three-Dimensional Variational Data Assimilation in a Limited-Area Weather Prediction Model and Comparison to E4DVar

2013 ◽  
Vol 141 (3) ◽  
pp. 900-917 ◽  
Author(s):  
Fuqing Zhang ◽  
Meng Zhang ◽  
Jonathan Poterjoy
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Weather Prediction ◽  
Three Dimensional ◽  
Variational Data Assimilation ◽  
Lead Times ◽  
Limited Area ◽  
Model Errors ◽  
Mean Square Errors

Abstract This study examines the performance of a hybrid ensemble-variational data assimilation system (E3DVar) that couples an ensemble Kalman filter (EnKF) with the three-dimensional variational data assimilation (3DVar) system for the Weather Research and Forecasting (WRF) Model. The performance of E3DVar and the component EnKF and 3DVar systems are compared over the eastern United States for June 2003. Conventional sounding and surface observations as well as data from wind profilers, aircraft and ships, and cloud-tracked winds from satellites, are assimilated every 6 h during the experiments, and forecasts are verified using standard sounding observations. Forecasts with 12- to 72-h lead times are found to have noticeably smaller root-mean-square errors when initialized with the E3DVar system, as opposed to the EnKF, especially for the 12-h wind and moisture fields. The E3DVar system demonstrates similar performance as an EnKF, while using less than half the number of ensemble members, and is less sensitive to the use of a multiphysics ensemble to account for model errors. The E3DVar system is also compared with a similar hybrid method that replaces the 3DVar component with the WRF four-dimensional variational data assimilation (4DVar) method (denoted E4DVar). The E4DVar method demonstrated considerable improvements over E3DVar for nearly all model levels and variables at the shorter forecast lead times (12–48 h), but the forecast accuracies of all three ensemble-based methods (EnKF, E3DVar, and E4DVar) converge to similar results at longer lead times (60–72 h). Nevertheless, all methods that used ensemble information produced considerably better forecasts than the two methods that relied solely on static background error covariance (i.e., 3DVar and 4DVar).

scholarly journals Influence of Assimilating Surface Observations on Numerical Prediction of Landfalls of Hurricane Katrina (2005) with an Ensemble Kalman Filter

2014 ◽  
Vol 142 (8) ◽  
pp. 2915-2934 ◽  
Author(s):  
Hailing Zhang ◽  
Zhaoxia Pu
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Hurricane Katrina ◽  
Ensemble Kalman Filter ◽  
Surface Wind ◽  
Initial Time ◽  
Filter Method ◽  
Low Level ◽  
The Impact ◽  
Surface Observations

Abstract A series of numerical experiments are conducted to examine the impact of surface observations on the prediction of landfalls of Hurricane Katrina (2005), one of the deadliest disasters in U.S. history. A specific initial time (0000 UTC 25 August 2005), which led to poor prediction of Hurricane Katrina in several previous studies, is selected to begin data assimilation experiments. Quick Scatterometer (QuikSCAT) ocean surface wind vectors and surface mesonet observations are assimilated with the minimum central sea level pressure and conventional observations from NCEP into an Advanced Research version of the Weather Research and Forecasting Model (WRF) using an ensemble Kalman filter method. Impacts of data assimilation on the analyses and forecasts of Katrina’s track, landfalling time and location, intensity, structure, and rainfall are evaluated. It is found that the assimilation of QuikSCAT and mesonet surface observations can improve prediction of the hurricane track and structure through modifying low-level thermal and dynamical fields such as wind, humidity, and temperature and enhancing low-level convergence and vorticity. However, assimilation of single-level surface observations alone does not ensure reasonable intensity forecasts because of the lack of constraint on the mid- to upper troposphere. When surface observations are assimilated with other conventional data, obvious enhancements are found in the forecasts of track and intensity, realistic convection, and surface wind structures. More importantly, surface data assimilation results in significant improvements in quantitative precipitation forecasts (QPFs) during landfalls.

scholarly journals Concentric Eyewall Formation in Typhoon Sinlaku (2008). Part I: Assimilation of T-PARC Data Based on the Ensemble Kalman Filter (EnKF)

2012 ◽  
Vol 140 (2) ◽  
pp. 506-527 ◽  
Author(s):  
Chun-Chieh Wu ◽  
Yi-Hsuan Huang ◽  
Guo-Yuan Lien
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Surface Wind ◽  
Measurement Data ◽  
Wrf Model ◽  
Weather Research And Forecasting ◽  
Secondary Eyewall Formation ◽  
Wind Structure ◽  
The Impact

Typhoon Sinlaku (2008) is a case in point under The Observing System Research and Predictability Experiment (THORPEX) Pacific Asian Regional Campaign (T-PARC) with the most abundant flight observations taken and with great potential to address major scientific issues in T-PARC such as structure change, targeted observations, and extratropical transition. A new method for vortex initialization based on ensemble Kalman filter (EnKF) data assimilation and the Weather Research and Forecasting (WRF) model is adopted in this study. By continuously assimilating storm positions (with an update cycle every 30 min), the mean surface wind structure, and all available measurement data, this study constructs a unique high-spatial/temporal-resolution and model/observation-consistent dataset for Sinlaku during a 4-day period. Simulations of Sinlaku starting at different initial times are further investigated to assess the impact of the data. It is striking that some of the simulations are able to capture Sinlaku’s secondary eyewall formation, while others starting the simulation earlier with less data assimilated are not. This dataset provides a unique opportunity to study the dynamical processes of concentric eyewall formation in Sinlaku. In Part I of this work, results from the data assimilation and simulations are presented, including concentric eyewall evolution and the precursors to its formation, while detailed dynamical analyses are conducted in follow-up research.

Sign in / Sign up

Export Citation Format

Share Document